The mockingbirds of the title are symbolic. The theme is that some creatures are helpless and do no one any harm, and they should be protected and not victimized.
Early on in the story, the Finch children get guns for Christmas and are warned never to kill a mockingbird.
When Atticus tells the children that it is a sin to kill a mockingbird, they ask Miss Maudie for an explanation.
Mockingbirds don't do one thing but make music for us to enjoy. They don't eat up people's gardens, don't nest in corncribs, they don't do one thing but sing their hearts out for us. (ch 10)
This poignant idea gets extended to the figurative mockingbirds in the story, including Boo Radley. Boo Radley is an innocent young man who is caught up in circumstances beyond his control. Because he is odd, it is easy to victimize and demonize him.
When Boo rescues Jem and Scout, Atticus convinces Heck Tate not to say anything. They do not want Boo to suffer any fame or notoriety, because he is so shy. Atticus asks Scout if she understands why they cannot tell anyone what Boo did. Her response brings the story full circle.
"Well, it'd be sort of like shootin' a mockingbird, wouldn't it?" (ch 30)
This demonstrates Scout’s maturity. She has come to learn empathy, and she realizes that Boo Radley did a heroic and remarkable thing in becoming their friend. Symbolically, he is a mockingbird.